Answer:
aₙ = a₁ . 5⁽ⁿ⁻¹⁾
Step-by-step explanation:
The first term in the sequence is a₁ = 6.
a₂ = 30. a₃ = 150.
We see that each consecutive term is multiplies by 5 to arrive at the next term.
That is: a₂ = 30 = a₁ . [tex]$ 5^{2 - 1} = 5 $[/tex] = 6.5 = 30.
Similarly, a₃ = 150 = 6 [tex]$ \times $[/tex] [tex]$ 5^{3 - 1} = 5^2 = 25 $[/tex]
Generalizing this, we have:
aₙ = a₁ . [tex]$ 5^{n - 1} $[/tex]
This is called the recursive formula of the sequence.
